This paper is concerned with the problem of quantifying the strength
of arguments in controversial debates, which we model as abstract argumentation
frameworks [Dung, 1995]. Standard approaches to abstract argumentation provide
only a qualitative account of the status of arguments, whereas numerical measures
of argument strength might provide a more precise evaluation of their individual
status. Intuitively, the strength of an argument in a debate essentially depends on
how a proponent of that argument would defend himself against the criticisms of
someone opposed to the argument. Since there can be many ways of defending and
attacking an opinion, we essentially conceive argument strength as an equilibrium
resulting from the interactions taking place between the opinions that a proponent
and an opponent of the argument could a priori embrace. More formally, we define
argument strength in terms of the value of a repeated two-person zero-sum strategic
game with imperfect information. Then, using the game-theoretic properties of
such games and notably the von Neumann minimax theorem [Neumann, 1928], we
establish and illustrate the main properties of this new argument strength measure.